The paper examines prioritization in a queuing system and analyzes whether, in the presence of heterogeneous customers and a costly sorting process, it pays to prioritize. In particular, in our model, the task of gathering information to prioritize/sort jobs consumes resources. We investigate a stylized model in which there are two classes of jobs -- one whose waiting cost is high, called urgent, and the other whose waiting cost is low, called non-urgent. There are two types of employees -- sorters who collect information on a job and then decide whether it is urgent or a non-urgent, and processors who execute the job or provide the service. This paper has three parts. In the first, we study a queuing process with a given exogenous budget. We compare two system designs, a sorter-plus-processor system in which some of the budget is allocated to sorters and the remainder to processors, and a processor-only system in which the entire budget is allocated to processors. We find that when the probability that the arrival is an urgent job has an intermediate value (neither too low nor too high), sorting is beneficial. We also conclude that there is a threshold cost ratio (ratio of waiting cost of urgent jobs to non-urgent jobs) such that if the cost ratio exceeds this threshold, sorting is beneficial and if it does not, it is not beneficial. In the second part, there is no budget, but we minimize the sum of labor costs and waiting costs, and show that both system designs have unique optimal labor costs. We then compare the optimal total costs of the two systems and find which one performs better. In both these parts, we just consider the "only-sorting" scenario in which the information collected by the sorter is just useful for sorting jobs. In the third part, we analyze the two systems in more general cases in which the information collected by the sorter is valuable to the processor and may reduce her processing time
